What name is shared by the star of an Irish sitcom starting in 2011, a woman who starred in a racially groundbreaking sitcom, the creator of which died in 2011, and the star of a successful US sitcom based on a British one?

I agree with the first part of the DaveBill's answer, Brendan O'Carroll but think the US sitcom is All In The Family starring Carroll O'Connor as Archie Bunker, as for the groundbreaking sitcom I haven't a clue.

Just out of interest, would the groundbreaking sitcom be 'Desmond's'? Or is it the one with a young Lenworth Henry? Or is it an American one? (Not that it matters, I think the question's been answered)

Carroll O'Connor was indeed Archie Bunker in that US version of "Till Death Us Do Part". The first US sitcom with a black woman "in a non-stereotypical role" according to Wikipedia was "Julia", starring Dihann Carroll. I've only heard of it because's its creator's obituary was in the paper last week. Well, DaveBill got the Carroll part from "Mrs Brown's Boys", so gets control of the remote...